Source: Question bank on challenging integral problems for high school students. An advanced level problem
Problem: Evaluate the indefinite integral: $$\int \frac{\mathrm dx}{(a+b\cos x)^2}$$ given that $a>b$
My try on it: It seems simple enough but upon a deeper look I can't find a suitable substitution for it. Not even going to try integrating by parts! Tried constructing a function whose integral is the one above. Gotten close results but not quite it. And that is not the correct approach anyway! Also tried using Partial fractions by constructing a function
$${1\over(a+by)^2} = {Ay+B\over(a+by)^2} + {Cy+D\over a+by}$$
Pretty unsure about this one. Am I going right or can you please suggest a better, quicker alternative. I can upload the answer if someone needs to refer it.